Fueling Innovation and Discovery The Mathematical Sciences in the 21st Century (2012) / Chapter Skim
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Bayesian Inference / Not an Enigma Anymore
Bayesian Inference / Not an Enigma Anymore
Pages 20-23
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From page 20... ...
It was won in part by a statistical method called Bayesian inference, which allowed code breakers to determine probabilistically which settings of the Enigma machine (which changed daily) were more likely than others (see Figure 6)
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From page 21... ...
But to a prior degree a Bayesian, it makes perfect sense; it means that you are willing to give 3-1 odds in a bet of belief in the on team A hypothesis you The key ingredient in Bayesian statistics is Bayes's rule (named after the Reverend Thomas Bayes, whose monograph on the subject was published posthumously in 1763)
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From page 22... ...
In the late 1980s, statisticians realized that a technique called Markov chain Monte Carlo provided a very efficient and general way to empirically sample a random distribution that is too complex to be expressed in a formula. Markov chain Monte Carlo had been developed in the 1950s by physicists who wanted to simulate random processes like the chain reactions of neutrons in a hydrogen bomb.
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From page 23... ...
For example, an experimenter might know that a parameter will be negative without knowing anything about the specific value of the parameter. Basic research in these areas will complement the application-specific research on problems like finding breast cancer genes or building robots and will therefore ensure that Bayesian inference continues to find a wealth of new applications.
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